**Explanation:**

**Introduction:**
Antibiotics are medications that are used to treat bacterial infections. They work by killing or inhibiting the growth of bacteria. However, not all diseases are caused by bacteria, and therefore, not all diseases can be cured by antibiotics.

**Explanation:**
Out of the diseases listed in the options, amoebiasis is the one that cannot be cured by taking antibiotics. Here's why:

1. **Plague:** Plague is caused by the bacterium Yersinia pestis. It can be treated with antibiotics such as streptomycin, gentamicin, or doxycycline. With prompt treatment, most people recover from the plague.

2. **Amoebiasis:** Amoebiasis is caused by the parasite Entamoeba histolytica. Antibiotics are not effective against parasites. The treatment for amoebiasis typically involves antiparasitic medications like metronidazole or tinidazole, which specifically target the parasite.

3. **Leprosy:** Leprosy is caused by the bacterium Mycobacterium leprae. It is treated with a combination of antibiotics such as dapsone, rifampicin, and clofazimine. Leprosy treatment usually requires long-term antibiotic therapy to completely eliminate the bacteria.

4. **Whooping cough:** Whooping cough, or pertussis, is caused by the bacterium Bordetella pertussis. Antibiotics such as azithromycin or erythromycin can be used to treat whooping cough, especially in the early stages of the infection.

Therefore, the correct answer is **(b) Amoebiasis**, as it is caused by a parasite and requires antiparasitic medications rather than antibiotics for treatment.